Just a thought...
Don't overlook the possibility of a loose connection.
Often when you "mess with it", you seem to get a temporary respite (until it loosens again?).

I've checked connections a few times. It was one of the first things I did when the problem first started. Re-checked everything when I put in the power supply. I always check connections when I have issues, I've even fixed a problem on old systems before because it was just a loose wire.

It's been almost 2 months since the last issue, and almost as long since I put in a better power supply.

For 2 months all has been quiet. It's doing it again. The other night it locked up completely and just now it restarted all by itself in the same manner as before.

This time, I can't view the system logs. When I try to open the Event Viewer, I just get a message after a few moments saying "Microsoft Management Console has stopped working..." and it closes. I'll try a proper restart to see if that gets working.

Maybe it's time I look into replacing that hard drive with an SSD.

Edit: A full shutdown and proper restart didn't get the Event Viewer to work. Still crashed. I looked at my notes, today's exactly 2 months since the last crash/random restart.

Regardless, I do believe this is some sort of hardware issue. Any failure (vid card, RAM, mobo, CMOS, CPU, etc.) can cause reboots. However, PSUs are the likeliest culprits.

Agree with Eric and others. Sounds more like a hardware issue than software, however nothing can be ruled out at this stage.

However, I would definitely see if you can use a Linux disk booted and left for hours or a couple days, to rule out Windows 10/Windows Updates as the culprit first since that would be the least expensive route.

Especially since the problem came back.

Let us know how that goes.

Digerati, on 01 December 2017 - 10:12 AM, said:

And for that matter, when you apply power to the computer, the HD will spin anyway even if you boot to the CD/DVD.

Very true. You could disconnect power to the suspected hard drive when you boot to a Linux cd/dvd and test it twice; once with hard drive connected and once with it disconnected.